Henri Poincaré provides an example in mathematical physics, as discussed by Thibault Damour and Howard Stein.
Poincarésaid in June 1905:
The essential point established by Lorentz is that the electromagneticfield equations are not altered by a certain transformation (which Ishall call after the name of Lorentz), which has the following form:\begin{align} x'&=kl(x+\epsilon t)\\ y'&=ly\\ z'&=lz\\ t'&=kl(t+\epsilon x) \end{align} where $x,y,z$ are the coordinates and$t$ the time before the transformation, and $x',y',z'$ and $t'$ afterthe transformation. Moreover, $\epsilon$ is a constant which definesthe transformation $k=1/\sqrt {1-\epsilon ^2}$ and $l$ is an arbitraryfunction of $\epsilon$.
One can see that in this transformation the $x$-axis plays aparticular role, but one can obviously construct a transformation inwhich this role would be played by any straight line through theorigin. The sum of all these transformations, together with the set ofall rotations of space, must form a group.
In a longer version of this paper from July 1905, Poincaréadded that this does not change the quadratic form written in different units as$x^2+y^2+z^2-t^2$ and that we can regard $x,y,z,t\sqrt{-1}$ as the coordinates in a 4-dimensional space, with the Lorentz transformation as a rotation of that space around the origin. Poincaré regarded this as only completing Lorentz's work "in a few points of detail"; this led to Albert Einstein saying that "for all his acuteness, Poincaré showed little understanding of the situation."
When Einstein saw the same mathematical properties, also in June 1905, he created the theory of special relativity.
